This invention relates to a product quality control system for controlling the manufacture of products, or in particular to a quality control system for products manufactured through a plurality of processes and supply chain elements.
A method and an apparatus for controlling the product quality on a semiconductor manufacturing line are disclosed in JP-A-2002-110493 (Patent Document 1) and JP-A-2000-252180 (Patent Document 2). These patents relate to a method and an apparatus for controlling the product quality based on the analysis of the causation connection of the product quality data and the manufacturing data. The product quality data to be analyzed is the electrical characteristics and yield of the semiconductor wafer, while the manufacturing data refers to the history of the manufacturing equipment, the manufacturing specification, the in-line measurement and the equipment route for the manufacturing processes and steps. As a method to analyze the causation connection, the multistage multivariate analysis (Y=A·X) is used with the product quality data as an object variable (Y) and the manufacturing data as an explanatory variable (X).
Specifically, first, in order to avoid the problem of incalculability and insufficient accuracy due to the multiple collinear phenomenon caused by the simultaneous change in a plurality of elements of the explanatory variable, the elements of the explanatory variable are divided into a few number of predetermined groups. Then, the multiple linear regression analysis (Yi=A·Xi) is applied to all the division groups, and the elements of the explanatory variable are reduced in each division group by the forward-backward stepwise selection. The explanatory variables thus reduced are subjected again to the multiple linear regression analysis repeatedly in multiple stages to extract an abnormal element.
As a product quality control technique for the manufacturing process of steel or the like, a method to analyze the causes of the defect of the manufacturing data from the product quality data is disclosed in JP-A-2003-114713 (Patent Document 3). The product quality data dealt with in Patent Document 3 concerns only the quality defect. Also, the multivariate process data is handled as the manufacturing data to be analyzed. In Patent Document 3, the principal component analysis of the manufacturing data is used as a method to analyze the causes of the quality defect. Specifically, the multivariate process data is converted into a few number of principal component scores due to linear combination by the principal component analysis. Then, the residual and the distance are calculated, and in the case where the calculation result is not included in the permissible range, the degree of contribution of each process data is calculated to extract a causative process data.
On the other hand, a technique for the automobile manufacturing line is described in JP-A-2002-251212 (Patent Document 4). Patent Document 4 discloses a method and a system for determining whether the substandard quality of high-ranked parts (module or product) manufactured by combining a plurality of types of low-ranked parts is caused by the defects of the low-ranked parts or the assembly process. The product quality data to be analyzed in Patent Document 4 is the vehicle body assembled by the completed product maker.
The information used for the low-ranked parts is the dimensions and the shape of the front and rear door units assembled by the assembler. The information on the lowest-ranked parts is the dimensions and shape of the door units handled by the parts maker. The cause of the substandard quality is determined by collation between the product and the quality data in each tier of the parts hierarchy, and as long as the parts are conforming in all the tiers of the hierarchy, it is determined that the substandard quality is caused by the assembly at the completed product maker.
A plurality of calculation methods of the correlation model (Y=A·X) of the object variable (Y) and the explanatory variable (X) based on the projection method to avoid the incalculability problem and the insufficient accuracy due to the multiple collinear phenomenon caused by the simultaneous change of a plurality of the elements of the explanatory variable are described in “Chemometrics, Data Analysis for the Laboratory and Chemical Plant”, WILEY (2003), pp. 412–415 (Nonpatent Document 1).
On the other hand, a graphical modeling method constituting one of the multivariate analysis methods in the statistical science is discussed in “Graphical Models”, OXFORD UNIVERSITY PRESS (1996), Steffen L. Lauritzen, p. 1 and pp. 123–157 (Nonpatent Document 2). Specifically, an outline of the mathematic foundation of the method to visually express an approximation model of a complicated connecting structure between a plurality of variates in the real world by a mathematic graph and search and verify the particular model from the partial correlation coefficient.